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 A318944 Number of Dyck paths with n nodes and altitude 4. 2
 0, 0, 0, 0, 1, 8, 32, 114, 376, 1177, 3549, 10406, 29861, 84249, 234502, 645625, 1761765, 4772534, 12851261, 34434561, 91890118, 244385617, 648139821, 1714976054, 4529163125, 11942440233, 31448759302, 82727323369, 217426319541, 571033273142 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 REFERENCES Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L. (2018). Enumerations of peaks and valleys on non-decreasing Dyck paths. Discrete Mathematics, 341(10), 2789-2807. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,-31,50,-36,8). FORMULA a(n) = 9*a(n-1) - 31*a(n-2) + 50*a(n-3) - 36*a(n-4) + 8*a(n-5) for n>9. - Colin Barker, Apr 11 2019 MAPLE (1-x)^2*x^4*(1+x-8*x^2+7*x^3)/(1-2*x)^3/(1-3*x+x^2) ; taylor(%, x=0, 30) ; gfun[seriestolist](%) ; # R. J. Mathar, Nov 25 2018 MATHEMATICA LinearRecurrence[{9, -31, 50, -36, 8}, {0, 0, 0, 0, 1, 8, 32, 114, 376, 1177}, 30] (* Harvey P. Dale, Nov 03 2019 *) PROG (PARI) concat([0, 0, 0, 0], Vec(x^4*(1 - x)^2*(1 + x - 8*x^2 + 7*x^3) / ((1 - 2*x)^3*(1 - 3*x + x^2)) + O(x^40))) \\ Colin Barker, Apr 11 2019 CROSSREFS A column of A318942. Sequence in context: A204643 A036393 A003201 * A196097 A234272 A269077 Adjacent sequences: A318941 A318942 A318943 * A318945 A318946 A318947 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Sep 18 2018 STATUS approved

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Last modified April 16 07:08 EDT 2024. Contains 371698 sequences. (Running on oeis4.)